EQUILIBRIUM OF A RIGID BODY
|
|
- Bryan George
- 5 years ago
- Views:
Transcription
1 EQUILIBRIUM OF A RIGID BODY Today s Objectives: Students will be able to a) Identify support reactions, and, b) Draw a free diagram.
2 APPLICATIONS A 200 kg platform is suspended off an oil rig. How do we determine the force reactions at the joints and the forces in the cables? How are the idealized model and the free body diagram used to do this? Which diagram above is the idealized model?
3 APPLICATIONS (continued) A steel beam is used to support roof joists. How can we determine the support reactions at A & B? Again, how can we make use of an idealized model and a free body diagram to answer this question?
4 CONDITIONS FOR RIGID-BODY EQUILIBRIUM (Section 5.1) Forces on a particle In contrast to the forces on a particle, the forces on a rigid-body are not usually concurrent and may cause rotation of the body (due to the moments created by the forces). For a rigid body to be in equilibrium, the net force as well as the net moment about any arbitrary point O must be equal to zero. å F = 0 and å M O = 0 Forces on a rigid body
5 THE PROCESS OF SOLVING RIGID BODY EQUILIBRIUM PROBLEMS For analyzing an actual physical system, first we need to create an idealized model. Then we need to draw a free-body diagram showing all the external (active and reactive) forces. Finally, we need to apply the equations of equilibrium to solve for any unknowns.
6 PROCEDURE FOR DRAWING A FREE BODY DIAGRAM (Section 5.2) Idealized model Free body diagram 1. Draw an outlined shape. Imagine the body to be isolated or cut free from its constraints and draw its outlined shape. 2. Show all the external forces and couple moments. These typically include: a) applied loads, b) support reactions, and, c) the weight of the body.
7 PROCEDURE FOR DRAWING A FREE BODY DIAGRAM (Section 5.2) (continued) Idealized model Free body diagram 3. Label loads and dimensions: All known forces and couple moments should be labeled with their magnitudes and directions. For the unknown forces and couple moments, use letters like A x, A y, M A, etc.. Indicate any necessary dimensions.
8 SUPPORT REACTIONS IN 2-D A few examples are shown above. Other support reactions are given in your textbook (in Table 5-1). As a general rule, if a support prevents translation of a body in a given direction, then a force is developed on the body in the opposite direction. Similarly, if rotation is prevented, a couple moment is exerted on the body.
9 EQUATIONS OF EQUILIBRIUM IN 2-D Today s Objectives: Students will be able to a) Apply equations of equilibrium to solve for unknowns, and, b) Recognize two-force members.
10 APPLICATIONS For a given load on the platform, how can we determine the forces at the joint A and the force in the link (cylinder) BC?
11 APPLICATIONS (continued) A steel beam is used to support roof joists. How can we determine the support reactions at each end of the beam?
12 EQUATIONS OF EQUILIBRIUM (Section 5.3) A body is subjected to a system of forces that lie in the x-y plane. When in equilibrium, the net force and net moment acting on the body are zero (as discussed earlier in Section 5.1). This 2-D condition can be represented by the three scalar equations: å F x = 0 å F y = 0 å M O = 0 Where point O is any arbitrary point. Please note that these equations are the ones most commonly used for solving 2-D equilibrium problems. There are two other sets of equilibrium equations that are rarely used. For your reference, they are described in the textbook. F 1 y O F 3 F 2 F 4 x
13 TWO-FORCE MEMBERS (Section 5.4) The solution to some equilibrium problems can be simplified if we recognize members that are subjected to forces at only two points (e.g., at points A and B). If we apply the equations of equilibrium to such a member, we can quickly determine that the resultant forces at A and B must be equal in magnitude and act in the opposite directions along the line joining points A and B.
14 EXAMPLE OF TWO-FORCE MEMBERS In the cases above, members AB can be considered as two-force members, provided that their weight is neglected. This fact simplifies the equilibrium analysis of some rigid bodies since the directions of the resultant forces at A and B are thus known (along the line joining points A and B).
15 STEPS FOR SOLVING 2-D EQUILIBRIUM PROBLEMS 1. If not given, establish a suitable x - y coordinate system. 2. Draw a free body diagram (FBD) of the object under analysis. 3. Apply the three equations of equilibrium (EofE) to solve for the unknowns.
16 IMPORTANT NOTES 1. If we have more unknowns than the number of independent equations, then we have a statically indeterminate situation. We cannot solve these problems using just statics. 2. The order in which we apply equations may affect the simplicity of the solution. For example, if we have two unknown vertical forces and one unknown horizontal force, then solving å F X = O first allows us to find the horizontal unknown quickly. 3. If the answer for an unknown comes out as negative number, then the sense (direction) of the unknown force is opposite to that assumed when starting the problem.
17 RIGID BODY EQUILIBRIUM IN 3-D (Sections ) Today s Objective: Students will be able to a) Identify support reactions in 3-D and draw a free body diagram, and, b) apply the equations of equilibrium.
18 APPLICATIONS Ball-and-socket joints and journal bearings are often used in mechanical systems. How can we determine the support reactions at these joints for a given loading?
19 SUPPORT REACTIONS IN 3-D (Table 5-2) A few examples are shown above. Other support reactions are given in your text book (Table 5-2). As a general rule, if a support prevents translation of a body in a given direction, then a reaction force acting in the opposite direction is developed on the body. Similarly, if rotation is prevented, a couple moment is exerted on the body by the support.
20 IMPORTANT NOTE A single bearing or hinge can prevent rotation by providing a resistive couple moment. However, it is usually preferred to use two or more properly aligned bearings or hinges. Thus, in these cases, only force reactions are generated and there are no moment reactions created.
21 EQULIBRIUM EQUATIONS IN 3-D (Section 5.6) As stated earlier, when a body is in equilibrium, the net force and the net moment equal zero, i.e., å F = 0 and å M O = 0. These two vector equations can be written as six scalar equations of equilibrium (EofE). These are å F X = å F Y = å F Z = 0 åm X = å M Y = å M Z = 0 The moment equations can be determined about any point. Usually, choosing the point where the maximum number of unknown forces are present simplifies the solution. Those forces do not appear in the moment equation since they pass through the point. Thus, they do not appear in the equation.
22 CONSTRAINTS FOR A RIGID BODY (Section 4.7) Redundant Constraints: When a body has more supports than necessary to hold it in equilibrium, it becomes statically indeterminate. A problem that is statically indeterminate has more unknowns than equations of equilibrium. Are statically indeterminate structures used in practice? Why or why not?
23 IMPROPER CONSTRAINTS Here, we have 6 unknowns but there is nothing restricting rotation about the x axis. In some cases, there may be as many unknown reactions as there are equations of equilibrium. However, if the supports are not properly constrained, the body may become unstable for some loading cases.
24 EXAMPLE Given:The cable of the tower crane is subjected to 840 N force. A fixed base at A supports the crane. Find: Reactions at the fixed base A. Plan: a) Establish the x, y and z axes. b) Draw a FBD of the crane. c) Write the forces using Cartesian vector notation. d) Apply the equations of equilibrium (vector version) to solve for the unknown forces.
25 EXAMPLE (continued) r BC = {12 i + 8 j - 24 k} m F = F [u BC ] N = 840 [12 i + 8 j - 24 k] / ( ( 24 2 )) ½ = {360 i + 24 j k} N F A = {A X i + A Y j + A Z k } N
26 EXAMPLE (continued) From EofE we get, F + F A = 0 {(360 + A X ) i + (240 + A Y ) j + ( A Z ) k} = 0 Solving each component equation yields A X = N, A Y = N, and A Z = 720 N.
27 EXAMPLE (continued) Sum the moments acting at point A. å M = M A + r AC F = 0 i j k = M AX i + M AY j + M AZ k = 0 = M AX i + M AY j + M AZ k i j = 0 M AX = 7200 N m, M AY = N m, and M AZ = 0 Note: For simpler problems, one can directly use three scalar moment equations, å M X = å M Y = å M Z = 0
28 Homework Problems 5-3, 5-21, 5-25, 5-32, 5-56
CHAPTER 2: EQUILIBRIUM OF RIGID BODIES
For a rigid body to be in equilibrium, the net force as well as the net moment about any arbitrary point O must be zero Summation of all external forces. Equilibrium: Sum of moments of all external forces.
More informationAnnouncements. Equilibrium of a Rigid Body
Announcements Equilibrium of a Rigid Body Today s Objectives Identify support reactions Draw a free body diagram Class Activities Applications Support reactions Free body diagrams Examples Engr221 Chapter
More informationEQUATIONS OF EQUILIBRIUM & TWO- AND THREE-FORCE MEMBERS
EQUATIONS OF EQUILIBRIUM & TWO- AND THREE-FORCE MEMBERS Today s Objectives: Students will be able to: a) Apply equations of equilibrium to solve for unknowns, and, b) Recognize two-force members. APPLICATIONS
More informationEquilibrium of a Rigid Body. Chapter 5
Equilibrium of a Rigid Body Chapter 5 Overview Rigid Body Equilibrium Free Body Diagrams Equations of Equilibrium 2 and 3-Force Members Statical Determinacy CONDITIONS FOR RIGID-BODY EQUILIBRIUM Recall
More informationEQUATIONS OF EQUILIBRIUM & TWO- AND THREE-FORCE MEMEBERS
EQUATIONS OF EQUILIBRIUM & TWO- AND THREE-FORCE MEMEBERS Today s Objectives: Students will be able to: a) Apply equations of equilibrium to solve for unknowns, and, b) Recognize two-force members. In-Class
More informationEQUATIONS OF EQUILIBRIUM & TWO- AND THREE-FORCE MEMBERS
EQUATIONS OF EQUILIBRIUM & TWO- AND THREE-FORCE MEMBERS Today s Objectives: Students will be able to: a) Apply equations of equilibrium to solve for unknowns b) Identify support reactions c) Recognize
More informationENGR-1100 Introduction to Engineering Analysis. Lecture 13
ENGR-1100 Introduction to Engineering Analysis Lecture 13 EQUILIBRIUM OF A RIGID BODY & FREE-BODY DIAGRAMS Today s Objectives: Students will be able to: a) Identify support reactions, and, b) Draw a free-body
More informationEngineering Mechanics Statics
Mechanical Systems Engineering _ 2016 Engineering Mechanics Statics 7. Equilibrium of a Rigid Body Dr. Rami Zakaria Conditions for Rigid-Body Equilibrium Forces on a particle Forces on a rigid body The
More informationEQUATIONS OF EQUILIBRIUM & TWO-AND THREE-FORCE MEMEBERS
EQUATIONS OF EQUILIBRIUM & TWO-AND THREE-FORCE MEMEBERS Today s Objectives: Students will be able to: a) Apply equations of equilibrium to solve for unknowns, and, b) Recognize two-force members. READING
More informationEQUATIONS OF EQUILIBRIUM & TWO- AND THREE-FORCE MEMEBERS
EQUATIONS OF EQUILIBRIUM & TWO- AND THREE-FORCE MEMEBERS Today s Objectives: Students will be able to: a) Apply equations of equilibrium to solve for unknowns, and b) Recognize two-force members. In-Class
More informationEngineering Mechanics: Statics in SI Units, 12e
Engineering Mechanics: Statics in SI Units, 12e 5 Equilibrium of a Rigid Body Chapter Objectives Develop the equations of equilibrium for a rigid body Concept of the free-body diagram for a rigid body
More informationEquilibrium of a Particle
ME 108 - Statics Equilibrium of a Particle Chapter 3 Applications For a spool of given weight, what are the forces in cables AB and AC? Applications For a given weight of the lights, what are the forces
More informationEQUILIBRIUM OF A RIGID BODY & FREE-BODY DIAGRAMS
Today s Objectives: Students will be able to: EQUILIBRIUM OF A RIGID BODY & FREE-BODY DIAGRAMS a) Identify support reactions, and, b) Draw a free-body diagram. In-Class Activities: Check Homework Reading
More information3.1 CONDITIONS FOR RIGID-BODY EQUILIBRIUM
3.1 CONDITIONS FOR RIGID-BODY EQUILIBRIUM Consider rigid body fixed in the x, y and z reference and is either at rest or moves with reference at constant velocity Two types of forces that act on it, the
More informationChapter Objectives. Copyright 2011 Pearson Education South Asia Pte Ltd
Chapter Objectives To develop the equations of equilibrium for a rigid body. To introduce the concept of the free-body diagram for a rigid body. To show how to solve rigid-body equilibrium problems using
More informationSTATICS. Bodies. Vector Mechanics for Engineers: Statics VECTOR MECHANICS FOR ENGINEERS: Design of a support
4 Equilibrium CHAPTER VECTOR MECHANICS FOR ENGINEERS: STATICS Ferdinand P. Beer E. Russell Johnston, Jr. Lecture Notes: J. Walt Oler Texas Tech University of Rigid Bodies 2010 The McGraw-Hill Companies,
More informationChapter 5: Equilibrium of a Rigid Body
Chapter 5: Equilibrium of a Rigid Body Chapter Objectives To develop the equations of equilibrium for a rigid body. To introduce the concept of a free-body diagram for a rigid body. To show how to solve
More informationIshik University / Sulaimani Architecture Department. Structure. ARCH 214 Chapter -5- Equilibrium of a Rigid Body
Ishik University / Sulaimani Architecture Department 1 Structure ARCH 214 Chapter -5- Equilibrium of a Rigid Body CHAPTER OBJECTIVES To develop the equations of equilibrium for a rigid body. To introduce
More informationChapter 5: Equilibrium of a Rigid Body
Chapter 5: Equilibrium of a Rigid Body Develop the equations of equilibrium for a rigid body Concept of the free-body diagram for a rigid body Solve rigid-body equilibrium problems using the equations
More informationStatics - TAM 211. Lecture 14 October 19, 2018
Statics - TAM 211 Lecture 14 October 19, 2018 Announcements Students are encouraged to practice drawing FBDs, writing out equilibrium equations, and solving these by hand using your calculator. Expending
More informationThe case where there is no net effect of the forces acting on a rigid body
The case where there is no net effect of the forces acting on a rigid body Outline: Introduction and Definition of Equilibrium Equilibrium in Two-Dimensions Special cases Equilibrium in Three-Dimensions
More informationLecture 14 February 16, 2018
Statics - TAM 210 & TAM 211 Lecture 14 February 16, 2018 SoonTrending.com Announcements Structured office hours of working through practice problems will be held during Sunday office hours, starting Sunday
More informationEQUILIBRIUM OF RIGID BODIES
EQUILIBRIUM OF RIGID BODIES Equilibrium A body in equilibrium is at rest or can translate with constant velocity F = 0 M = 0 EQUILIBRIUM IN TWO DIMENSIONS Case where the force system acting on a rigid
More informationPAT 101 FUNDAMENTAL OF ENGINEERING MECHANICS EQUILIBREQUILIBRIUM OF A RIGID BODY IUM OF A RIGID BODY
PAT 101 FUNDAMENTAL OF ENGINEERING MECHANICS EQUILIBREQUILIBRIUM OF A RIGID BODY IUM OF A RIGID BODY MARDHIAH FARHANA BINT OMAR Week 5-6 EQUILIBRIUM OF A RIGID BODY Conditions for Rigid Equilibrium Free-Body
More informationTheory of structure I 2006/2013. Chapter one DETERMINACY & INDETERMINACY OF STRUCTURES
Chapter one DETERMINACY & INDETERMINACY OF STRUCTURES Introduction A structure refers to a system of connected parts used to support a load. Important examples related to civil engineering include buildings,
More informationEquilibrium of a Rigid Body. Engineering Mechanics: Statics
Equilibrium of a Rigid Body Engineering Mechanics: Statics Chapter Objectives Revising equations of equilibrium of a rigid body in 2D and 3D for the general case. To introduce the concept of the free-body
More informationENGI 1313 Mechanics I
ENGI 1313 Mechanics I Lecture 25: Equilibrium of a Rigid Body Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland spkenny@engr.mun.ca
More informationENGR-1100 Introduction to Engineering Analysis. Lecture 23
ENGR-1100 Introduction to Engineering Analysis Lecture 23 Today s Objectives: Students will be able to: a) Draw the free body diagram of a frame and its members. FRAMES b) Determine the forces acting at
More informationEquilibrium. Rigid Bodies VECTOR MECHANICS FOR ENGINEERS: STATICS. Eighth Edition CHAPTER. Ferdinand P. Beer E. Russell Johnston, Jr.
Eighth E 4 Equilibrium CHAPTER VECTOR MECHANICS FOR ENGINEERS: STATICS Ferdinand P. Beer E. Russell Johnston, Jr. Lecture Notes: J. Walt Oler Texas Tech University of Rigid Bodies Contents Introduction
More informationOutline: Frames Machines Trusses
Outline: Frames Machines Trusses Properties and Types Zero Force Members Method of Joints Method of Sections Space Trusses 1 structures are made up of several connected parts we consider forces holding
More informationEngineering Mechanics: Statics in SI Units, 12e
Engineering Mechanics: Statics in SI Units, 12e 3 Equilibrium of a Particle 1 Chapter Objectives Concept of the free-body diagram for a particle Solve particle equilibrium problems using the equations
More informationME Statics. Structures. Chapter 4
ME 108 - Statics Structures Chapter 4 Outline Applications Simple truss Method of joints Method of section Germany Tacoma Narrows Bridge http://video.google.com/videoplay?docid=-323172185412005564&q=bruce+lee&pl=true
More informationLecture 23. ENGR-1100 Introduction to Engineering Analysis FRAMES S 1
ENGR-1100 Introduction to Engineering Analysis Lecture 23 Today s Objectives: Students will be able to: a) Draw the free body diagram of a frame and its members. FRAMES b) Determine the forces acting at
More information6.6 FRAMES AND MACHINES APPLICATIONS. Frames are commonly used to support various external loads.
6.6 FRAMES AND MACHINES APPLICATIONS Frames are commonly used to support various external loads. How is a frame different than a truss? How can you determine the forces at the joints and supports of a
More informationSupport Idealizations
IVL 3121 nalysis of Statically Determinant Structures 1/12 nalysis of Statically Determinate Structures nalysis of Statically Determinate Structures The most common type of structure an engineer will analyze
More informationSRSD 2093: Engineering Mechanics 2SRRI SECTION 19 ROOM 7, LEVEL 14, MENARA RAZAK
SRSD 2093: Engineering Mechanics 2SRRI SECTION 19 ROOM 7, LEVEL 14, MENARA RAZAK SIMPLE TRUSSES, THE METHOD OF JOINTS, & ZERO-FORCE MEMBERS Today s Objectives: Students will be able to: a) Define a simple
More informationEQUILIBRIUM OF A PARTICLE, THE FREE-BODY DIAGRAM & COPLANAR FORCE SYSTEMS
EQUILIBRIUM OF PRTICLE, THE FREE-BODY DIGRM & COPLNR FORCE SYSTEMS Today s Objectives: Students will be able to : a) Draw a free body diagram (FBD), and, b) pply equations of equilibrium to solve a 2-D
More informationSIMPLE TRUSSES, THE METHOD OF JOINTS, & ZERO-FORCE MEMBERS
SIMPLE TRUSSES, THE METHOD OF JOINTS, & ZERO-FORCE MEMBERS Today s Objectives: Students will be able to: a) Define a simple truss. b) Determine the forces in members of a simple truss. c) Identify zero-force
More informationAnnouncements. Trusses Method of Joints
Announcements Mountain Dew is an herbal supplement Today s Objectives Define a simple truss Trusses Method of Joints Determine the forces in members of a simple truss Identify zero-force members Class
More informationCheck Homework. Reading Quiz Applications Equations of Equilibrium Example Problems Concept Questions Group Problem Solving Attention Quiz
THREE-DIMENSIONAL FORCE SYSTEMS Today s Objectives: Students will be able to solve 3-D particle equilibrium problems by a) Drawing a 3-D free body diagram, and, b) Applying the three scalar equations (based
More informationMEE224: Engineering Mechanics Lecture 4
Lecture 4: Structural Analysis Part 1: Trusses So far we have only analysed forces and moments on a single rigid body, i.e. bars. Remember that a structure is a formed by and this lecture will investigate
More informationTUTORIAL SHEET 1. magnitude of P and the values of ø and θ. Ans: ø =74 0 and θ= 53 0
TUTORIAL SHEET 1 1. The rectangular platform is hinged at A and B and supported by a cable which passes over a frictionless hook at E. Knowing that the tension in the cable is 1349N, determine the moment
More informationThe centroid of an area is defined as the point at which (12-2) The distance from the centroid of a given area to a specified axis may be found by
Unit 12 Centroids Page 12-1 The centroid of an area is defined as the point at which (12-2) The distance from the centroid of a given area to a specified axis may be found by (12-5) For the area shown
More informationWhen a rigid body is in equilibrium, both the resultant force and the resultant couple must be zero.
When a rigid body is in equilibrium, both the resultant force and the resultant couple must be zero. 0 0 0 0 k M j M i M M k R j R i R F R z y x z y x Forces and moments acting on a rigid body could be
More informationWhen a rigid body is in equilibrium, both the resultant force and the resultant couple must be zero.
When a rigid body is in equilibrium, both the resultant force and the resultant couple must be zero. 0 0 0 0 k M j M i M M k R j R i R F R z y x z y x Forces and moments acting on a rigid body could be
More informationChapter 6: Structural Analysis
Chapter 6: Structural Analysis Chapter Objectives To show how to determine the forces in the members of a truss using the method of joints and the method of sections. To analyze the forces acting on the
More informationEquilibrium of Rigid Bodies
Equilibrium of Rigid Bodies 1 2 Contents Introduction Free-Bod Diagram Reactions at Supports and Connections for a wo-dimensional Structure Equilibrium of a Rigid Bod in wo Dimensions Staticall Indeterminate
More informationChapter 7 INTERNAL FORCES
Chapter 7 INTERNAL FORCES READING QUIZ 1. In a multiforce member, the member is generally subjected to an internal. A) normal force B) shear force C) bending moment D) All of the above. 2. In mechanics,
More informationStatics. Phys101 Lectures 19,20. Key points: The Conditions for static equilibrium Solving statics problems Stress and strain. Ref: 9-1,2,3,4,5.
Phys101 Lectures 19,20 Statics Key points: The Conditions for static equilibrium Solving statics problems Stress and strain Ref: 9-1,2,3,4,5. Page 1 The Conditions for Static Equilibrium An object in static
More informationINTERNAL FORCES Today s Objective: Students will be able to: 1. Use the method of sections for determining internal forces in 2-D load cases.
INTERNAL FORCES Today s Objective: Students will be able to: 1. Use the method of sections for determining internal forces in 2-D load cases. In-Class Activities: Check Homework, if any Reading Quiz Applications
More informationChapter 7: Bending and Shear in Simple Beams
Chapter 7: Bending and Shear in Simple Beams Introduction A beam is a long, slender structural member that resists loads that are generally applied transverse (perpendicular) to its longitudinal axis.
More informationEngineering Mechanics: Statics STRUCTURAL ANALYSIS. by Dr. Ibrahim A. Assakkaf SPRING 2007 ENES 110 Statics
CHAPTER Engineering Mechanics: Statics STRUCTURAL ANALYSIS College of Engineering Department of Mechanical Engineering Tenth Edition 6a by Dr. Ibrahim A. Assakkaf SPRING 2007 ENES 110 Statics Department
More informationSample 5. Determine the tension in the cable and the horizontal and vertical components of reaction at the pin A. Neglect the size of the pulley.
Sample 1 The tongs are designed to handle hot steel tubes which are being heat-treated in an oil bath. For a 20 jaw opening, what is the minimum coefficient of static friction between the jaws and the
More informationContinuing Education Course #207 What Every Engineer Should Know About Structures Part B Statics Applications
1 of 6 Continuing Education Course #207 What Every Engineer Should Know About Structures Part B Statics Applications 1. As a practical matter, determining design loads on structural members involves several
More informationSTATICS. Bodies VECTOR MECHANICS FOR ENGINEERS: Ninth Edition CHAPTER. Ferdinand P. Beer E. Russell Johnston, Jr.
N E 4 Equilibrium CHAPTER VECTOR MECHANICS FOR ENGINEERS: STATICS Ferdinand P. Beer E. Russell Johnston, Jr. Lecture Notes: J. Walt Oler Texas Tech University of Rigid Bodies 2010 The McGraw-Hill Companies,
More informationChapter - 1. Equilibrium of a Rigid Body
Chapter - 1 Equilibrium of a Rigid Body Dr. Rajesh Sathiyamoorthy Department of Civil Engineering, IIT Kanpur hsrajesh@iitk.ac.in; http://home.iitk.ac.in/~hsrajesh/ Condition for Rigid-Body Equilibrium
More informationENGR-1100 Introduction to Engineering Analysis. Lecture 20
ENGR-1100 Introduction to Engineering Analysis Lecture 20 Today s Objectives: THE METHOD OF SECTIONS Students will be able to determine: 1. Forces in truss members using the method of sections. In-Class
More informationLecture 20. ENGR-1100 Introduction to Engineering Analysis THE METHOD OF SECTIONS
ENGR-1100 Introduction to Engineering Analysis Lecture 20 THE METHOD OF SECTIONS Today s Objectives: Students will be able to determine: 1. Forces in truss members using the method of sections. In-Class
More informationF R. + F 3x. + F 2y. = (F 1x. j + F 3x. i + F 2y. i F 3y. i + F 1y. j F 2x. ) i + (F 1y. ) j. F 2x. F 3y. = (F ) i + (F ) j. ) j
General comments: closed book and notes but optional one page crib sheet allowed. STUDY: old exams, homework and power point lectures! Key: make sure you can solve your homework problems and exam problems.
More informationTo show how to determine the forces in the members of a truss using the method of joints and the method of sections.
5 Chapter Objectives To show how to determine the forces in the members of a truss using the method of joints and the method of sections. To analyze the forces acting on the members of frames and machines
More informationthree Equilibrium 1 and planar trusses ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SPRING 2015 lecture ARCH 614
ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SPRING 2015 lecture three equilibrium and planar trusses Equilibrium 1 Equilibrium balanced steady resultant of forces
More informationPLANAR KINETIC EQUATIONS OF MOTION: TRANSLATION
PLANAR KINETIC EQUATIONS OF MOTION: TRANSLATION Today s Objectives: Students will be able to: 1. Apply the three equations of motion for a rigid body in planar motion. 2. Analyze problems involving translational
More informationEngineering Mechanics: Statics. Chapter 7: Virtual Work
Engineering Mechanics: Statics Chapter 7: Virtual Work Introduction Previous chapters-- FBD & zero-force and zero-moment equations -- Suitable when equilibrium position is known For bodies composed of
More informationSpring 2018 Lecture 28 Exam Review
Statics - TAM 210 & TAM 211 Spring 2018 Lecture 28 Exam Review Announcements Concept Inventory: Ungraded assessment of course knowledge Extra credit: Complete #1 or #2 for 0.5 out of 100 pt of final grade
More informationENGR-1100 Introduction to Engineering Analysis. Lecture 19
ENGR-1100 Introduction to Engineering Analysis Lecture 19 SIMPLE TRUSSES, THE METHOD OF JOINTS, & ZERO-FORCE MEMBERS Today s Objectives: Students will be able to: In-Class Activities: a) Define a simple
More informationEng Sample Test 4
1. An adjustable tow bar connecting the tractor unit H with the landing gear J of a large aircraft is shown in the figure. Adjusting the height of the hook F at the end of the tow bar is accomplished by
More information7 STATICALLY DETERMINATE PLANE TRUSSES
7 STATICALLY DETERMINATE PLANE TRUSSES OBJECTIVES: This chapter starts with the definition of a truss and briefly explains various types of plane truss. The determinancy and stability of a truss also will
More informationChapter 6: Structural Analysis
Chapter 6: Structural Analysis APPLICATIONS Trusses are commonly used to support a roof. For a given truss geometry and load, how can we determine the forces in the truss members and select their sizes?
More informationPLANAR KINETIC EQUATIONS OF MOTION: TRANSLATION (Sections ) Today s Objectives: Students will be able to: a) Apply the three equations of
PLANAR KINETIC EQUATIONS OF MOTION: TRANSLATION (Sections 17.2-17.3) Today s Objectives: Students will be able to: a) Apply the three equations of motion for a rigid body in planar motion. b) Analyze problems
More informationES226 (01) Engineering Mechanics: Statics Spring 2018 Lafayette College Engineering Division
ES226 (01) Engineering Mechanics: Statics Spring 2018 Lafayette College Engineering Division Exam 1 Study Guide Exam 1: Tuesday, February 6, 2018 7:30 to 8:30pm Kirby Room 104 Exam Format: 50 minute time
More informationPlane Trusses Trusses
TRUSSES Plane Trusses Trusses- It is a system of uniform bars or members (of various circular section, angle section, channel section etc.) joined together at their ends by riveting or welding and constructed
More informationEquilibrium Equilibrium and Trusses Trusses
Equilibrium and Trusses ENGR 221 February 17, 2003 Lecture Goals 6-4 Equilibrium in Three Dimensions 7-1 Introduction to Trusses 7-2Plane Trusses 7-3 Space Trusses 7-4 Frames and Machines Equilibrium Problem
More informationLOVELY PROFESSIONAL UNIVERSITY BASIC ENGINEERING MECHANICS MCQ TUTORIAL SHEET OF MEC Concurrent forces are those forces whose lines of action
LOVELY PROFESSIONAL UNIVERSITY BASIC ENGINEERING MECHANICS MCQ TUTORIAL SHEET OF MEC 107 1. Concurrent forces are those forces whose lines of action 1. Meet on the same plane 2. Meet at one point 3. Lie
More informationFRAMES AND MACHINES Learning Objectives 1). To evaluate the unknown reactions at the supports and the interaction forces at the connection points of a
FRAMES AND MACHINES Learning Objectives 1). To evaluate the unknown reactions at the supports and the interaction forces at the connection points of a rigid frame in equilibrium by solving the equations
More informationStatics: Lecture Notes for Sections
Chapter 6: Structural Analysis Today s Objectives: Students will be able to: a) Define a simple truss. b) Determine the forces in members of a simple truss. c) Identify zero-force members. READING QUIZ
More informationWORCESTER POLYTECHNIC INSTITUTE
WORCESTER POLYTECHNIC INSTITUTE MECHANICAL ENGINEERING DEPARTMENT STRESS ANALYSIS ES-2502, C 2012 Lecture 02: Internal Forces 13 January 2012 General information Instructor: Cosme Furlong HL-151 (508)
More informationVector Mechanics: Statics
PDHOnline Course G492 (4 PDH) Vector Mechanics: Statics Mark A. Strain, P.E. 2014 PDH Online PDH Center 5272 Meadow Estates Drive Fairfax, VA 22030-6658 Phone & Fax: 703-988-0088 www.pdhonline.org www.pdhcenter.com
More informationSection 6: 6: Kinematics Kinematics 6-1
6-1 Section 6: Kinematics Biomechanics - angular kinematics Same as linear kinematics, but There is one vector along the moment arm. There is one vector perpendicular to the moment arm. MA F RMA F RD F
More informationEngineering Mechanics: Statics in SI Units, 12e
Engineering Mechanics: Statics in SI Units, 12e 3 Equilibrium of a Particle Chapter Objectives To introduce the concept of the free-body diagram for a particle To show how to solve particle equilibrium
More informationChapter 04 Equilibrium of Rigid Bodies
Chapter 04 Equilibrium of Rigid Bodies Application Engineers designing this crane will need to determine the forces that act on this body under various conditions. 4-2 Introduction For a rigid body, the
More informationStatic Equilibrium. University of Arizona J. H. Burge
Static Equilibrium Static Equilibrium Definition: When forces acting on an object which is at rest are balanced, then the object is in a state of static equilibrium. - No translations - No rotations In
More informationAnnouncements. Equilibrium of a Particle in 2-D
nnouncements Equilibrium of a Particle in 2-D Today s Objectives Draw a free body diagram (FBD) pply equations of equilibrium to solve a 2-D problem Class ctivities pplications What, why, and how of a
More informationCourse Overview. Statics (Freshman Fall) Dynamics: x(t)= f(f(t)) displacement as a function of time and applied force
Course Overview Statics (Freshman Fall) Engineering Mechanics Dynamics (Freshman Spring) Strength of Materials (Sophomore Fall) Mechanism Kinematics and Dynamics (Sophomore Spring ) Aircraft structures
More informationEquilibrium of rigid bodies Mehrdad Negahban (1999)
Equilibrium of rigid bodies Mehrdad Negahban (1999) Static equilibrium for a rigid body: A body (or any part of it) which is currently stationary will remain stationary if the resultant force and resultant
More informationMethod of Sections for Truss Analysis
Method of Sections for Truss Analysis Notation: (C) = shorthand for compression P = name for load or axial force vector (T) = shorthand for tension Joint Configurations (special cases to recognize for
More informationSTATICS. FE Review. Statics, Fourteenth Edition R.C. Hibbeler. Copyright 2016 by Pearson Education, Inc. All rights reserved.
STATICS FE Review 1. Resultants of force systems VECTOR OPERATIONS (Section 2.2) Scalar Multiplication and Division VECTOR ADDITION USING EITHER THE PARALLELOGRAM LAW OR TRIANGLE Parallelogram Law: Triangle
More informationENGINEERING MECHANICS BAA1113
ENGINEERING MECHANICS BAA1113 Chapter 3: Equilibrium of a Particle (Static) by Pn Rokiah Bt Othman Faculty of Civil Engineering & Earth Resources rokiah@ump.edu.my Chapter Description Aims To explain the
More informationCEE 271: Applied Mechanics II, Dynamics Lecture 25: Ch.17, Sec.4-5
1 / 36 CEE 271: Applied Mechanics II, Dynamics Lecture 25: Ch.17, Sec.4-5 Prof. Albert S. Kim Civil and Environmental Engineering, University of Hawaii at Manoa Date: 2 / 36 EQUATIONS OF MOTION: ROTATION
More informationModule 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method
Module 2 Analysis of Statically Indeterminate Structures by the Matrix Force Method Lesson 11 The Force Method of Analysis: Frames Instructional Objectives After reading this chapter the student will be
More informationPLANAR KINETIC EQUATIONS OF MOTION: TRANSLATION
PLANAR KINETIC EQUATIONS OF MOTION: TRANSLATION Today s Objectives: Students will be able to: 1. Apply the three equations of motion for a rigid body in planar motion. 2. Analyze problems involving translational
More informationCalculate the force F needed to produce a horizontal component of 300 N on the sledge (1)
1. A heavy sledge is pulled across snowfields. The diagram shows the direction of the force F exerted on the sledge. Once the sledge is moving, the average horizontal force needed to keep it moving at
More informationMoment Distribution The Real Explanation, And Why It Works
Moment Distribution The Real Explanation, And Why It Works Professor Louie L. Yaw c Draft date April 15, 003 To develop an explanation of moment distribution and why it works, we first need to develop
More informationMOMENT ABOUT AN AXIS
Today s Objectives: MOMENT ABOUT AN AXIS Students will be able to determine the moment of a force about an axis using a) scalar analysis, and b) vector analysis. In-Class Activities: Applications Scalar
More informationMechanics of Materials
Mechanics of Materials 2. Introduction Dr. Rami Zakaria References: 1. Engineering Mechanics: Statics, R.C. Hibbeler, 12 th ed, Pearson 2. Mechanics of Materials: R.C. Hibbeler, 9 th ed, Pearson 3. Mechanics
More informationME 230 Kinematics and Dynamics
ME 230 Kinematics and Dynamics Wei-Chih Wang Department of Mechanical Engineering University of Washington Lecture 6: Particle Kinetics Kinetics of a particle (Chapter 13) - 13.4-13.6 Chapter 13: Objectives
More information2008 FXA THREE FORCES IN EQUILIBRIUM 1. Candidates should be able to : TRIANGLE OF FORCES RULE
THREE ORCES IN EQUILIBRIUM 1 Candidates should be able to : TRIANGLE O ORCES RULE Draw and use a triangle of forces to represent the equilibrium of three forces acting at a point in an object. State that
More informationChapter 8. Rotational Equilibrium and Rotational Dynamics. 1. Torque. 2. Torque and Equilibrium. 3. Center of Mass and Center of Gravity
Chapter 8 Rotational Equilibrium and Rotational Dynamics 1. Torque 2. Torque and Equilibrium 3. Center of Mass and Center of Gravity 4. Torque and angular acceleration 5. Rotational Kinetic energy 6. Angular
More informationFE Sta'cs Review. Torch Ellio0 (801) MCE room 2016 (through 2000B door)
FE Sta'cs Review h0p://www.coe.utah.edu/current- undergrad/fee.php Scroll down to: Sta'cs Review - Slides Torch Ellio0 ellio0@eng.utah.edu (801) 587-9016 MCE room 2016 (through 2000B door) Posi'on and
More informationChapter 12. Static Equilibrium and Elasticity
Chapter 12 Static Equilibrium and Elasticity Static Equilibrium Equilibrium implies that the object moves with both constant velocity and constant angular velocity relative to an observer in an inertial
More information1. Please complete the following short problems.
Name 1. Please complete the following short problems. For parts 1A and 1B, we will consider three M88 recovery vehicles pulling an M1 tank back onto the road as shown below. F2 F1 50 M88 #1 50 M88 #2 y
More information